This report presents a new statistical approach to the image segmentation problem. By modelling image data as a Markov random field characterized by a Gibbs distribution, a dynamic programming algorithm is developed. The primary contribution of the paper is this new near optimal method for processing scenes described by the non-causal Gibbs model. The report is organized as follows. Section 2 defines the segmentation problem in a statistical framework, introduces some notation, and presents some background on Markov random fields. Section 3 then presents the dynamic programming algorithm in detail for the case of segmenting images consisting of uniform intensity regions in high levels of additive white Gaussian noise. Section 4 presents results of applying the algorithms to some experimentally generated images consistent with this model as well as some synthetic aperture radar images which are clearly inconsistent with the assumed model. These results clearly demonstrate the applicability of the technique to realistic data as well as the robustness of the algorithm with respect to modelling assumptions. In Section 5, some comments and concluding remarks are given, and extensions to this work which are in progress are briefly outlined.